To address the first need, a large sample of 456 galaxies from [1]} and completeness
measurements from [2]} are adopted. Details of this sample are given below.
The large size of and the data available for the sample necessitates simple estimates of
\(j\) . Therefore, we estimate \(j\)  as \(2 V_{\rm flat} r_d\) , where \(V_{\rm flat}\)  is the rotation velocity on
the flat part of the rotation curve and \(r_d\)  is the scale-length of the galaxy disc. This approximation
is exact for an exponential disc and a flat rotation curve. Uncertainties in estimates of
\(j\)  are \(\sim 15\) %, which are dominated by errors in measurements of \(r_s\)  (mainly due
to errors in sky background subtraction) and galaxy distances.
There are two minor effects on estimates of \(j\) , which we do not take into account,
but which work in opposite directions.
On the one hand, galaxies have rising rotation curves in their centres, and this causes the formula to slightly overestimate \(j\) .
On the other hand, most galaxies are expected to have extended gas discs, but with very little mass, which
would cause the formula to slightly underestimate \(j\) .
